I have a Raspberry Pi, but I'm currently using it for other things (it's plugged into my router providing DNS and DHCP, as well as a web server). I've thought about doing what you're suggesting, though I haven't taken much time to dig into it yet.
I'm sure it can be done, provided that you have the time and patience to learn how to set it all up.
Newegg has a temp/humidity sensor for $15 -https://www.newegg.com/p/2DS-007X-00659
A Pi 3 B+ with case and power, $55 -
https://www.pishop.us/product/raspberry-pi-3-b-plus-budget-kit/ (Doesn't include the MicroSD card)
You might need longer cables for the sensors, depending on the conditions in the place you're trying to monitor (I doubt the Pi would appreciate excessive temperature swings or humidity, though a more robust case could probably mitigate some of that). The components above are just examples, no idea if they are the best options price-wise or otherwise. The big expense will be the Pi itself...the peripherals are (generally) cheap.
It would be a decent amount of work on your part, you have to plan out where the sensors will be, where the Pi would be installed, and how to connect them to power (and probably your LAN). You then have to learn how to read data from the sensors and write it out to a data file. After that, you can decide how you want to process the data - there are various libraries out there to help with data visualization, or you could just
feed it into a spreadsheet and manually process it (but what's the fun in that, when you could make the computer do it for you?). As far as timing goes, there's really no limit. As long as your power stays on and nothing eats the wires or anything, you're "constrained" by the size of the SD card that you installed, which, unless you buy a tiny card that can barely hold the operating system,
should hold plenty of data - text is small, and it can be compressed to even smaller sizes. If you run out of space on the pi, just push it over the LAN to another computer, or get a bigger SD card, or plug a drive into the pi (though be careful with that, though, you may run yourself out of power).
I would love to actually do this someday, but I have kids and
chickens and gardens and a house to take care of, so it probably won't make it near the priority list for a while.